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Chinese Physics Letters

Scaling exponent for 3-state Potts model on 3-dimensional random triangle lattice

Chen Tian-Lun, Huang Wuqun

Published Dec 1, 1990• 1 citation
Publisher

Abstract

An optimal Monte Carlo renormalization group method is applied to 3-state Potts model on 3-dimensional random triangle lattice. The scaling exponent ν of the first order phase transition of this model has been obtained. In the disorder phase ν = 0.369(±0.044), y T = 1/ν = 2.71(±0.32), in the order phase ν = 0.393(±0.048), y T = 2.54(±0.31). They approximate to the prediction of the scaling theory.

DOI
10.1088/0256-307x/7/12/002

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An optimal Monte Carlo renormalization group method is applied to 3-state Potts model on 3-dimensional random triangle lattice. The scaling exponent ν of the first order phase transition of this model has been obtained. In the disorder phase ν = 0.369(±0.044), y T = 1/ν = 2.71(±0.32), in the order phase ν = 0.393(±0.048), y T = 2.54(±0.31). They approximate to the prediction of the scaling theory.
Phase transitions in the two-dimensional ferromagnetic Potts model with the number of spin states q = 3 on a triangular lattice were studied using Monte-Carlo method. The systems of linear size L = 20–120 were considered. Using the method of the fourth-order Binder cumulants, it was demonstrated that the second order phase transition is observed in the two-dimensional ferromagnetic Potts model. The static critical exponents for the heat capacity α, susceptibility γ, magnetization β and correlation radius ν were calculated based on the finite-dimensional scaling theory.
Monte Carlo simulations are performed to analyze phase transitions in three-dimensional systems described by the 3-state Potts model with nonmagnetic impurities. Numerical results are presented for systems with spin concentrations p = 1.00, 0.95, 0.90, 0.80, 0.70, and 0.65 on lattices of size L varying between 20 and 44. Binder’s cumulant analysis shows that the introduction of quenched disorder in the form of non-magnetic impurities induces a crossover from first-order to second-order phase transition. The finite-size scaling method is used to calculate the static critical exponents α, γ, β, and ν for specific heat, susceptibility, magnetization, and correlation length, respectively.
By introducing a small amount of non-magnetic impurities into an antiferromagnetic (AF) two-dimensional (2D) Potts model on a triangular lattice it is that the impurities in spin systems described by this model result in the change of a first order to a second-order phase transition. The systems with linear sizes L × L = N, L = 9-144 are considered. Investigations are performed using the standard Metropolis algorithm along with Monte-Carlo single-cluster Wolff algorithm. On the basis of the theory of finite-size scaling, critical exponents (CE) are calculated: the heat capacity α, the susceptibility γ, the order parameter β, and the CE of the correlation radius ν.
The critical behavior of the three-dimensional random-bond Potts model for large state numbers with q=16 and q=32 is studied by the finite-time dynamics combining with Monte Carlo renormalization group method. The correlation length and dynamic exponents as well as the critical temperatures are calculated through reducing the influence of finite-size effects. According to the variations of critical exponents with disorder amplitude, we identify the asymptotic critical exponents with ν=0.424(14), z=3.03(12) and find that they are q-independent. The results further confirm that the intrinsic ν, instead of finite-size one, can escape the bound ν>2/d suggested previously.